Time-dependent optimal control of a SEITR spreading model with hesitation and truth mechanisms

Yuzhen Zhao; Jinling Wang; Jiarong Li; Yuzhen Zhao; Jinling Wang; Jiarong Li

doi:10.3934/math.2026873

AIMS Mathematics

2026, Volume 11, Issue 7: 21541-21569. doi: 10.3934/math.2026873

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Research article

Time-dependent optimal control of a SEITR spreading model with hesitation and truth mechanisms

1.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2.
School of Science, Jimei University, Xiamen 361021, China
3.
College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

Received: 04 May 2026 Revised: 07 July 2026 Accepted: 10 July 2026 Published: 20 July 2026
MSC : 34D05, 37N20

This paper introduces a hesitation mechanism and true information spreaders to establish a Susceptible-Exposed-Infected-Truth-spreader-Recovered (SEITR) rumor propagation model, aiming to reveal how true information spreading influences rumor diffusion. First, based on the Routh-Hurwitz criterion and Lyapunov functions, the local asymptotic stability and global asymptotic stability of the system are proved respectively. Second, the Pontryagin minimum principle is applied to design the optimal control strategy, where key parameters are set as time-dependent functions, and the flexible control of the rumor propagation proportion is realized by dynamically adjusting control variables. Finally, numerical simulations verify the theoretical findings, which show that increasing the true information spreaders and blocking rumor transformation paths can effectively suppress rumor spread.
- rumor spreading,
- true information,
- basic reproduction number,
- stability analysis,
- optimal control
Citation: Yuzhen Zhao, Jinling Wang, Jiarong Li. Time-dependent optimal control of a SEITR spreading model with hesitation and truth mechanisms[J]. AIMS Mathematics, 2026, 11(7): 21541-21569. doi: 10.3934/math.2026873

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Abstract

This paper introduces a hesitation mechanism and true information spreaders to establish a Susceptible-Exposed-Infected-Truth-spreader-Recovered (SEITR) rumor propagation model, aiming to reveal how true information spreading influences rumor diffusion. First, based on the Routh-Hurwitz criterion and Lyapunov functions, the local asymptotic stability and global asymptotic stability of the system are proved respectively. Second, the Pontryagin minimum principle is applied to design the optimal control strategy, where key parameters are set as time-dependent functions, and the flexible control of the rumor propagation proportion is realized by dynamically adjusting control variables. Finally, numerical simulations verify the theoretical findings, which show that increasing the true information spreaders and blocking rumor transformation paths can effectively suppress rumor spread.

References

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